David T. Sandwell and Walter H. F. Smith

We are constructing a complete bathymetric map of the
oceans at a 3-10 km resolution by combining all of the available depth
soundings collected over the past 30 years with high resolution marine
gravity information provided by the Geosat, ERS-1/2, and Topex/Poseidon
altimeters. Detailed bathymetry is essential for understanding physical
oceanography and marine geophysics. Currents and tides are controlled by
the overall shapes of the ocean basins as well as the smaller sharp ocean
ridges and seamounts. Because erosion rates are low in the deep oceans,
detailed bathymetry reveals the mantle convection patterns, the plate boundaries,
the cooling/subsidence of the oceanic lithosphere, the oceanic plateaus,
and the distribution of off-ridge volcanoes. Current global digital bathymetry
maps (e.g. ETOPO-5) lack many important details such as a 400 km-long ridge
that rises to within 135 m of sea level (Figure 1). Moreover, they are
contaminated by long-wavelength errors (~2000 km) which prevent accurate
identification of seafloor swells associated with mantle plumes [Smith,
1993].

The tasks include:

* Accumulate all available depth soundings collected
over the past 30 years. (funded by NSF)
* Use the short wavelength (< 160 km) satellite gravity information
to interpolate between sparse ship soundings.
* Improve the resolution of the marine gravity field using enhanced estimates
along repeat altimeter profiles together with the dense altimeter measurements.
* Refine/Improve bathymetric predictionsusing the improved resolution
gravity field and also by investigating computer-intensive methods for
bathymetric prediction such as inverse theory.
* Produce a Globe of the Earth similar to the globe of Venus prepared
by the NASA Magellan investigation. This will also include the best available
digital land data.

Figure 1. (top) Seafloor depth based on ETOPO-5 lacks
the topographic expression of a 400 km long ridge as well as the rugged
topography of the Eltanin and Udintsev Fracture Zone Systems. The ridge
(53S, 140W, minumum depth 135 m) was first surveyed by a French expedition
in December of 1995. These topographic features effect the flow of the
the Antarctic Circumploar Current.
(middle) Predicted seafloor depth based on ship soundings and declassified
Geosat/GM data. The Sub-Antarctic Front (SAF-red) [Gille, 1994]
passes directly over the NW-trending ridge. The Polar Front (PF) is centered
on the 6000m deep valley of the Udintsev transform fault.
(bottom) Ship soundings used in the bathymetric prediction. Predicted depths
are constrained to agree with measured depths along these tracklines.

A detailed knowledge of topography is fundamental to
the understanding of most earth processes. On the land, weather and climate
are controlled by topography on scales ranging from large continental land
masses to small mountain valleys. The land is shaped by tectonics, erosion,
and sedimentation and thus detailed topography is an essential component
of any geological investigation. Hydrogeologic and biological processes
are also largely controlled by local relief. The planned Shuttle mission
to map land topography at 30 m horizontal resolution will provide much
of the detailed information for land studies.

In the Oceans, detailed bathymetry is also essential for
understanding physical oceanography and marine geophysics. Currents and
tides are controlled by the overall shapes of the ocean basins as well
as the smaller sharp ocean ridges and seamounts (Figure 1). Because erosion
and sedimentation rates are low in the deep oceans, detailed bathymetry
reveals the mantle convection patterns, the plate boundaries, the cooling/subsidence
of the oceanic lithosphere, the oceanic plateaus, and the distribution
of off-ridge volcanoes. Finally biological processes are largely controlled
by ocean depth and terrain. In contrast to the Shuttle mission which can
recover the land topography in 10 days, it would take approximatelt 125
ship-years to map the ocean basins at a 100 m horizontal resolution. Here
we propose to map the topography of the ocean basins at a 3-10 km resolution
using data collected by satellite altimeters and shipborn echo sounders.
This is a diverse effort that is currently partly funded by the Marine
Geology and Geophysics Division Program at NSF and was partly funded under
the NASA Global Geodynamics Program.

Now is the time to undertake this bathymetric mapping
because radar altimeters aboard the ERS-1/2, Geosat, and Topex/Poseidon
spacecraft have surveyed the marine gravity field over nearly all of the
world's oceans to a high accuracy and spatial resolution. On March 15,
1995 ERS-1 completed its dense mapping (~8 km track spacing at equator)
of the marine gravity between latitudes of +81.5. On July 28, 1995
all of the Geosat altimeter data were declassified (~4 km track spacing
at the equator; latitudes between +72). Moreover, the Topex/Poseidon
altimeter has accumulated many years of data having exceptional quality.
With NASA and other funding we have assimilated most of these data into
a global marine gravity anomaly grid (Figure 2) [Sandwell and Smith,
1996].

In the wavelength band 15 to 200 km, variations in gravity
anomaly are highly correlated with seafloor topography. Since many southern
ocean areas and some northern ocean areas are sparsely surveyed, these
new satellite altimeter data reveal many previously unsurveyed features
such as ridge axes, seamounts and fracture zones.

The conceptual approach is to use the sparse depth soundings
to constrain the long-wavelength depth while the shorter-wavelength topography
is predicted from the downward-continued satellite gravity measurements
[Smith and Sandwell, 1994]. Over the short wavelength band, the
topography/gravity ratio is regionally calibrated using available soundings.
We have found that major errors in the ETOPO-5 bathymetric model make it
unsuitable for either constraining the long-wavelength depths or for calibrating
the topography/gravity ratio. Thus for an accurate prediction, it is essential
to go back to the raw ship soundings.

CLEANING AND RESCUE OF SHIP SOUNDINGS

This Ship Track Map has been sectioned into 16 clickable
regions.
Clicking on a given region will produce an expanded view of that portion
of the map.

Data quality is the most important aspect of bathymetric
prediction. High resolution satellite gravity data is needed not only to
interpolate among the sparse soundings but also to identify which soundings
are bad. Many soundings from remote areas of the oceans were collected
before shipboard computers and satellite navigation were available. Moreover,
all of the ship sounding data were collected over a 30 year period on a
variety of ships from many countries and with many different chief scientists
aboard. Thus the quality of the data is highly variable and many entire
cruises or sections of cruises are bad [Smith, 1993]; only the most
recent (since ~1987) GPS-navigated multibeam data are reliable. Typical
errors include: navigation errors, digitizing errors, typographical errors
due to hand entry of older sounding, reporting the data in fathoms instead
of meters, incorrect sound velocity measurements and even computer errors
in reading punch cards One bad section of a cruise in an isolated region
will introduce a seafloor topographic feature that does not exist. Some
named examples are the Islas Orcadas Seamounts in the Weddell Sea and the
Novara Knoll in the Southern Indian Ocean [Canadian Hydrographic Service,
1984]. The high resolution gravity fields provides the information needed
to assess the accuracy of the ship sounding data. Our approach is to identify
the bad cruises through a comparison with an initial prediction based on
the gravity and either eliminate them or attempt to fix problem areas (data
rescue); rescue is especially important for soundings that fill a large
data gap. We maintain 4 data bases of standard underway geophysical data
(navigation, depth, gravity, and magnetics) in a GMTPLUS-format that is
easily assessable through GMT routines. There is a lot of overlap among
the data bases although each contains some unique cruises. Some statistics
on the number of good and bad cruises in each data base follows

The automation, maintenance, and rescue of the ship data
is largely funded by the NSF Division of Ocean Sciences. In addition to
these data we are preparing for the possible declassification of a the
US Navy Ocean Survey data [Medea Report, 1995].

Data preparation and assembly is an ongoing process; the
current data are sufficiently good to construct a global bathymetric grid.
Here is one recipe (Nettleton's Method) that we are developing.

NETTLETON'S METHOD

1) Grid available bathymetric soundings on a 2 minute
Mercator grid that matches our gravity anomaly grid. To avoid seams, all
work is done on a global grid between latitudes of +72deg. Coastline
points from GMT provide the zero-depth estimates. A finite-difference,
minimum-curvature routine is used to interpolate the global grid [Smith
and Wessel, 1990]. This gridding program requires at least 256 Mbytes
of computer memory.

2) Separate the grid into low-pass and high-pass
components using a Gaussian filter (0.5 gain at 160 km). Filtering and
downward continuation are performed with a multiple strip, 2-D FFT that
spans 0-360deg longitude to avoid Greenwich edge effects.

3) Form high-pass filtered gravity using the same
Gaussian filter.

4) Downward continue the high-pass filtered gravity
to the low-pass filtered bathymetry assuming Laplace's equation
is appropriate. A depth-dependent Wiener filter is used to stabilize the
downward continuation.

5) Accumulate high-pass filtered soundings and
corresponding high-pass filtered/downward-continued gravity into
small (160 km) overlapping areas and perform a robust regression analysis.
In sediment-free areas, the topography/gravity transfer function should
be flat and equal to 1/2[pi]G[Delta][rho] so in the space domain,
a linear regression is appropriate. This works well on young seafloor but
not on old seafloor where sediment cover destroys the correlation between
topography and gravity. In these cases we assume the seafloor is flat and
set the topography/gravity ratio to zero. Finally there are intermediate
cases where topographic depressions will be sediment filled while the highs
protrude above the sediments so the topography/gravity relationship is
non-linear. It is these partially sedimented areas that make the bathymetric
problem difficult and inherently non-linear. Continental margins and shelves
pose similar problems.

6) Regional topography/gravity ratio estimates
are gridded and multiplied by the high-pass filtered/downward-continued
gravity to form high-pass filtered predicted bathymetry.

7) The total predicted bathymetry is equal to the
sum of the high-pass filtered predicted bathymetry and the low-pass
filtered bathymetry.

8) Finally, the pixels constrained by ship soundings or
coastline data are reset to the measured values and the finite-difference,
minimum curvature routine is used to perturb the predicted values toward
the measured values. Measured depths are flagged so they can be extracted
separately. This final step dramatically increases the accuracy and resolution
of the bathymetric grid in well surveyed areas so it agrees with the best
hand-contoured bathymetric charts.